In industrial settings, control systems are used to monitor and control inventories of industrial and chemical processes and the like. Typically, the control system performs these functions using field devices distributed at key locations in the industrial process coupled to the control circuitry in the control room by a process control loop. The term “field device” refers to any device that performs a function in a distributed control or process monitoring system used in the measurement, control, and monitoring of industrial processes. Typically, field devices are characterized by their ability to operate outdoors for extended periods of time, such as years. Thus, a field device is able to operate in a variety of climatological extremes, including severe temperature extremes and extremes in humidity. Moreover, field devices are able to function in the presence of significant vibration, such as vibration from adjacent machinery. Further, field devices may also operate in the presence of electromagnetic interference.
One example of a field device is a multivariable process fluid flow device, such as that sold under the trade designation Model 3051 SMV Multivariable Transmitter by Emerson Process Management of Chanhassen, Minn. Multivariable process fluid flow devices can compute mass flow rate through differential producers for liquids and gases.
For differential producers, the mass flow rate is given by the following equation:Qm=N×Cd×Ed2×Y1×√{square root over (ρ)}×√{square root over (ΔP)}  Eq. 1
The following nomenclature is generally accepted with respect to the flow equation:    Qm=mass flow rate (mass/time)    QE=energy flow rate (energy/time)    QV=volumetric flow rate (length3/time)    P=static pressure (force/length2)    T=temperature (degrees)    ΔP=differential pressure across the primary element (force/length2)    N=units conversion factor (units vary)    Cd=primary element discharge coefficient (dimensionless)    d=primary element throat diameter (length)    D=pipe diameter (length)    E=velocity approach factor, (1/(1−(d/D)4)1/2) (dimensionless)    Y1=gas expansion factor, =1.0 for liquids (dimensionless)    ρ=fluid density (mass/length3)    μ=fluid viscosity (mass/length-time)    RD=pipe Reynolds number (dimensionless)    H=enthalpy (energy/mass)
Many of the flow quantities are dependent on other quantities. For example, the discharge coefficient Cd is a function of the Reynolds number. The Reynolds number is a function of the mass flow rate, the fluid viscosity and the pipe diameter. The thermal expansion effect Ed2 is a function of temperature. The gas expansion factor, Y1, is a function of differential pressure ΔP divided by the static pressure. Fluid density ρ and the compressibility factor Z are functions of static pressure and temperature. Fluid viscosity μ is a function of temperature. Enthalpy, H, is a function of static pressure and temperature.
As a result of the complexities and inter-related dependencies of the flow equation, the calculation of the flow rate has generally required some sort of iterative algorithm. One way of approaching this is to use the direct substitution approach outlined in AGA Report No. 3, Part 4 where it states that the first step is to guess a discharge coefficient value. Then the flow rate or Reynolds number is solved based on a set of static pressure (P), differential pressure (DP), and temperature (T) values. Using the resulting Reynolds number, a new discharge coefficient value is calculated and compared with the initial guess. If the result of this comparison is within a predefined limit, the newly calculated discharge coefficient is assumed to be the final value. If not, a new value of Reynolds number is calculated, followed by a new discharge coefficient value which are compared with the previous values. This process is repeated until the result of successive calculations of the discharged coefficient is within the predefined tolerance. This whole process, including the initial guess, is then repeated for the next set of pressure, differential pressure, and temperature values. This approach has the advantage of being simple to program. Its main disadvantage is the potentially large number of iterations required to reach a converged solution of the flow equation.
An alternative approach, again outlined in AGA Report No. 3, is to use a more sophisticated algorithm such as the Newton-Raphson algorithm. The overall approach still requires starting with an initial guess but the Newton-Raphson algorithm, which requires additional computations, converges more rapidly than the direct substitution method. The disadvantage of this approach is the additional computations required. Existing multivariable transmitters, including the 3095MV, use some version of the algorithms described above.
Both of the techniques described above require some form of iteration and convergence within a specified limit before the flow output is solved. Consequently, the overall time required to solve the flow computation, and subsequently provide the flow output, can be a number of iterations. Existing devices are generally able to provide a flow output value on the order of every 400 milliseconds. In controlling the flow of process fluids, any delay in providing a process fluid value, such as flow, can add instability or other deleterious effects to the overall process fluid control. Accordingly, there is a need to provide process fluid flow values, such as mass flow, volumetric flow, and energy flow as quickly as possible.
Two-wire field transmitters operating on limited power budgets generally need to minimize the computations. The power budget limitation is due to the desire for process devices to operable solely from power received through a process communication loop. The current can be as little at 3.6 mA and the voltage is generally constrained (to about 10 volts) as well. The current can actually be slightly less than 3.6 mA if digital signaling (such as that in accordance with the Highway Addressable Remote Transducer protocol) is used. Accordingly, process fluid flow transmitters are generally required to be operable on as little 30 milliwatts. Consequently, the general approach is to use simpler computational algorithms at the expense of computational speed and overall flowmeter response.